The specifics of the answer are impossible for us to provide, since it depends on processing that person's entire credit report. A single change in one factor may affect one person more or less than another person. And, it depends on what data a given credit bureau actually has for that person, and which credit scoring model they're using.
That said, we can speak in generic terms.
The factor you're referencing is called a "hard pull." When you apply for credit, the lender will pull your credit report in order to use it in making their decision on your application. This is referred to as a "hard pull" - and is different than if you or another entity pulls your report for non-decision purposes (i.e. just to check your score for your own information, or a bank pulling it for marketing purposes, etc). These other credit reports are referred to as "soft pulls" - although a hard pull and a soft pull will contain the same information, they're categorized differently based on the reason they're being pulled for. This is an important distinction because only hard pulls impact your credit score.
So, how much does a hard pull impact your score? Generally, it's a low- to medium-impact factor, though if your score is already low, you may be fighting for every point and even just a few points can make a difference.
You also seem to be asking, for how long does a hard pull impact your score? This varies depending on the model used as well, but generally hard pulls stay on your report for two years but only impact your score for one year.
Those questions out of the way, you're also asking about how multiple hard pulls impact your score. The good news is, banks and credit bureaus understand that consumers are likely to do at least a little shopping-around when looking for a loan, so multiple hard pulls in a short period of time will be condensed into a single event. In other words, if you go to four banks on the same day to apply for the same type of loan, you'll only see one hit to your score. The timeframe for bundling varies from model to model (it could be as short as 14 days or as much as 45 days). Also, there are cases where the way a bank requests your hard pull causes it to not be included in the bundling, so it's worth checking your score after you shop around to make sure this happened correctly - and if not, you can ask the credit bureau and/or the banks to adjust their reporting.
Finally, you're describing a scenario where someone is denied multiple times for credit applications. It's important to note that the decision made on a loan does not directly impact your score. In other words, if you're denied a loan, or you are approved for a loan but do not accept it, those two scenarios will have the same impact to your score (from the hard pull). Of course, if you accept a loan, the loan itself will be reported and will impact your score, but the approval vs denial does not directly have any impact.
